Equational theories of endomorphism monoids of categories with a topological flavor

It is shown that the endomorphism monoids of the category of all 2-cobordisms do not have finitely axiomatizable equational theories. The same holds for the topological annular category and various quotients of the latter, like the affine Temperley-Lieb category. Analogous results are obtained for versions with the algebraic signature enriched by involutions. Von-Neumann-regular extensions of these categories are also considered.

This is a joint work with Karl Auinger (University of Vienna).